Species Distribution Modelling

Russell Dinnage

• Sometimes called Environmental Niche Models (ENMs, I prefer SDM)
• Possible the most well-developed application of classic Data Science and Machine Learning (ML) in Biology
• They take in data on the environment at different sites or parts of a landscape and try predict where (or when, or how many) organisms will occur there. Data on the species themselves can also be used
• Traditionally done on single species at a time, but ‘joint’ species distribution models are increasingly common

• To make an SDM you use a Data Science workflow
• The final model used to predict species occurrence is fit using Machine Learning techniques
• A Data Science workflow has two major components:
  • Data
  • a Model

• Data Processing Steps

• Model Building

• Data feeds into Models

• Models inform Data processing steps

1. A Question
2. Collect Data
3. Munge / Clean Data
4. Transform Data for Model
5. Analyze Data using Model
6. Tune Model
7. Validate / Test Model
8. Interpret Model

1. A Question
2. Collect Data
3. Munge / Clean Data
4. Transform Data for Model
5. Analyze Data using Model
6. Tune Model
7. Validate / Test Model
8. Interpret Model

• We have covered some of this already
• We will cover the rest in the next 4 weeks

• Encodes a relationship between a set of inputs and outputs
• For an SDM this is a (potentially complex and nonlinear) function that takes environmental variables as input and its output is an occurrence pattern (could be abundance, probability, suitability, etc.)
• Different Models differ in their assumptions, or ‘inductive biases’, and their parameters
• Models are ‘fit’ to data
  • Parameters are chosen based on how well the Model’s output matches the real data
  • This is an optimization problem

The Linear Model

• Models outputs as a ‘linear’ function of inputs
• Inputs are ‘predictor’ variables
• Outputs are predictions, and they are compared to ‘response’ variable(s)
• Assumes responses are a additive linear function of predictors

Setup

library(sdmpack)
library(tidyverse)
library(tidymodels)

• Base R has a good collection of statistical methods including the linear model.
• RF_abund has data on the abundance of different reef species at different reefs around the world

data("RF_abund")
RF_abund

• First let’s choose a fish species to model
• Thalassoma pavo: Ornate Wrasse

fish_dat <- RF_abund %>%
  filter(SpeciesName == "Thalassoma pavo")

• lm() is the basic linear model function in R.
• Let’s do a linear model on our fish species with temperature as a predictor

mod <- lm(
  AbundanceAdult40 ~ MeanTemp_CoralWatch, 
  data = fish_dat)

mod <- lm(
  AbundanceAdult40 ~ MeanTemp_CoralWatch, 
  data = fish_dat)

• A formula is a special data structure in R
• It is specified using an expression of this form: lhs ~ rhs, where lhs stands for Left Hand Side, and rhs stands for Right Hand Side.
• Formulas compactly express a relationship between variables: lhs contains ‘response’ variables that we wish to model as a function of the variables on the rhs: the ‘predictor’ variable
• Both lhs and rhs can contain multiple variables and function calls (we will see examples of that later on)
• Though a formula can be missing lhs, they must always have a ~ and a rhs (~ rhs is a valid formula)

ggplot(fish_dat, aes(x = MeanTemp_CoralWatch, y = AbundanceAdult40)) +
  geom_smooth(method = lm, se = FALSE, color = "red") + geom_point() + theme_minimal()

It is much easier to tell if the model is useful at all by visualizing.

• This model is not a good fit, and there might be some other problems
  • Models have assumptions
  • Does our data fit the assumptions?
• I won’t go through all linear model assumption, but one is that the distribution of the data is not too extreme (skewed, or with long tails)

Distribution of Abundance:

 hist(fish_dat$AbundanceAdult40, breaks = 100)

• One way to ‘fix’ the data is to transform it, for example:

 hist(log(fish_dat$AbundanceAdult40), breaks = 50)

However the main problem seems to stem from the fact that a line is not a good description on the response. Therefore, most SDM methods that are actually used allow for non-linear relationships. In this case (and many cases), some kind of hump shaped function might make sense.

• tidymodels is an R package for statistical and machine learning models
• It shares the philosophy of programming and data analysis with tidyverse
• It has functions that mirror the step of Data Science that I presented earlier
• Like tidyverse it is a meta-package, bundling several other packages together

• parsnip separates the model ‘structure’ from the implementation
• It unifies inputs and outputs, so that it is simple to switch between different modelling methods without writing new code

• A model is fit using the fit() function
• parsnip is designed work with pipe operators (%>% or |>)

mod_pars <- linear_reg(engine = "lm") %>%
  fit(AbundanceAdult40 ~ MeanTemp_CoralWatch,
      data = fish_dat)
mod_pars

• Parameters are extracted with the tidy() function.

mod_summ <- tidy(mod_pars)
mod_summ

• Visualize the fit by prediction

preds <- predict(mod_pars, newdata = fish_dat)
preds
pred_dat <- fish_dat %>%
  bind_cols(preds)

• Now that the model is specified in parsnip, it is easy to change our model to one that can model nonlinear relationships easily. Let’s try doing a gradient boosted decision tree (you don’t need to know what that is for now).

mod_pars2 <- boost_tree(mode = "regression") %>%
  fit(AbundanceAdult40 ~ MeanTemp_CoralWatch,
      data = fish_dat)
mod_pars2

An important concept in Data Science and Machine Learning is the idea of overfitting. The above model appears to ‘overfit’ the data – its predictions jump around wildly to try and fit each individual data point. But this in not likely to generalize well if applied to a new dataset. We reduce overfitting by tuning the ‘hyper-parameters’ of the algorithm to make it produce ‘smoother’ predictions. Smoothed prediction are more likely to generalize better to new datasets. This is accomplished using a method called cross-validation, which we will cover in depth in Week 7.

Introducing the Pine Rocklands of South Florida

• Unique to South Florida
• High species diversity
• Open canopy forests dominated by Slash Pine
• Fire dependent ecosystem
• One of the most critically endanger ecosystems in the world
• Why?
  • Pine Rocklands central range is in the middle of Miami!
  • The only large patch remaining is in Everglades National Park

Image citation:

Trotta, Lauren B., et al. “Community phylogeny of the globally critically imperiled pine rockland ecosystem.” American journal of botany 105.10 (2018): 1735-1747.

• The FIU Preserve on campus has one of the few remaining patches of Pine Rockland in Miami-Dade
• In 2016 FIU conducted a prescribed burn to help restore this ecosystem of local importance

• I propose we do one big group project on the Pine Rocklands in weeks 11-16
• We will start here in lecture – I will use data on plants in the Pine Rockland for my examples in the next few weeks.
• For the final project, each of you can choose a species from the Pine Rocklands (or a few species) to run a SDM on and use it to make predictions. What is the past and future of Pine Rockland species?
• You will all follow the same steps of good Data Science
• You can work in groups or on your own, it is your decision
• At the end of the semester we will combine everyone’s SDMs into a prediction for the whole Pine Rockland community (or at least 18-30 species worth)

We will start by extracting data from this:

• I will start using that data for example in class next week.
• Next class we will be working on the Week 5 Assignment (you can start today).
• Next week we will cover:
  • How to go from abundance data to presence / absence (e.g. occurrences)
  • How to include data preprocessing and model fitting in one workflow using tidymodels
  • A little bit of ecological niche theory to understand what SDMs represent and why they are important